In a proposed hybrid vehicle, an internal combustion engine and a motor MG1 are connected via a planetary gear unit to a driveshaft, which is linked with an axle via a gear mechanism, and a motor MG2 is connected to the driveshaft (see, for example, Japanese Patent Laid-Open Gazette No. H11-93727). This prior art hybrid vehicle stops the operation of the engine in response to an engine stop request on condition that the vehicle speed is within a preset range, while continuing the operation of the engine on condition that the vehicle speed is out of the preset range. Such engine stop control aims to prevent the driver from feeling the shock of backlash or gear rattle in the gear mechanism.